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A time–distance diagram is a chart with two axes: one for time, the other for location. The units on either axis depend on the type of project: time can be expressed in minutes (for overnight construction of railroad modification projects such as the installation of switches) or years (for large construction projects); the location can be (kilo)meters, or other distinct units (such as ...
From the geometry shown in the diagram above, the following variables are defined: rod length (distance between piston pin and crank pin) crank radius (distance between crank center and crank pin, i.e. half stroke) crank angle (from cylinder bore centerline at TDC)
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
The graph in the figure is a plot of speed versus time. Distance covered is the area under the line. Each time interval is coloured differently. The distance covered in the second and subsequent intervals is the area of its trapezium, which can be subdivided into triangles as shown.
A Dead Reckoning, DR, is calculated by using a previously determined position on a chart, and advancing that position based on known or estimated speed over a set amount of time. This can be calculated by using the formula Speed = Distance ÷ Time. [3] Once an advance position has been plotted, then set and drift can be factored in.
The speed attained during free fall is proportional to the elapsed time, and the distance traveled is proportional to the square of the elapsed time. [39] Importantly, the acceleration is the same for all bodies, independently of their mass. This follows from combining Newton's second law of motion with his law of universal gravitation.